Question

express as a single logarithm 3 loga (2x+1) - 2 loga (2x-1) +2

Answer 1

Answer:

Step-by-step explanation:

$3 \log_{a} (2x+1)=\log_{a}(2x+1)^{3}$

$2 \log_{a}(2x-1)=\log_{a}(2x-1)^{2}$

$2=\log_{a}(a^{2})$

So the expression can be expressed as a single logarithm as follows:

$3\log_{a}(2x+1)-2\log_{a}(2x-1)+2=\log_{a}(2x+1)^{3}-\log_{a}(2x-1)^{2}+\log_{a}a^{2}$

$3\log_{a}(2x+1)-2\log_{a}(2x-1)+2=\log_{a}\left(\frac{(2x+1)^{3}a^{2}}{(2x-1)^{2}}\right)$